The Dirichlet problem for elliptic systems with data in Köthe function spaces
Genre
Journal ArticleDate
2016-01-01Author
Martell, JMMitrea, D
Mitrea, I
Mitrea, M
Subject
Dirichlet problemsecond-order elliptic system
nontangential maximal function
Hardy-Littlewood maximal operator
Poisson kernel
Green function
Kothe function space
Muckenhoupt weight
Lebesgue space
variable exponent Lebesgue space
Lorentz space
Zygmund space
Orlicz space
Hardy space
Beurling algebra
Hardy-Beurling space
semigroup
Fatou type theorem
Permanent link to this record
http://hdl.handle.net/20.500.12613/5746
Metadata
Show full item recordDOI
10.4171/rmi/903Abstract
© 2016 European Mathematical Society. We show that the boundedness of the Hardy-Littlewood maximal operator on a Kothe function space X and on its Kothe dual X is equivalent to the well-posedness of the X-Dirichlet and X-Dirichlet problems in Rn + in the class of all second-order, homogeneous, elliptic systems, with constant complex coefficients. As a consequence, we obtain that the Dirichlet problem for such systems is well-posed for boundary data in Lebesgue spaces, variable exponent Lebesgue spaces, Lorentz spaces, Zygmund spaces, as well as their weighted versions. We also discuss a version of the aforementioned result which contains, as a particular case, the Dirichlet problem for elliptic systems with data in the classical Hardy space H1, and the Beurling-Hardy space HAp for p € (1,∞). Based on the well-posedness of the Lp-Dirichlet problem we then prove the uniqueness of the Poisson kernel associated with such systems, as well as the fact that they generate a strongly continuous semigroup in natural settings. Finally, we establish a general Fatou type theorem guaranteeing the existence of the pointwise nontangential boundary trace for null-solutions of such systems.Citation to related work
European Mathematical Society Publishing HouseHas part
Revista Matematica IberoamericanaADA compliance
For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.eduae974a485f413a2113503eed53cd6c53
http://dx.doi.org/10.34944/dspace/5728
Scopus Count
Collections
Related items
Showing items related by title, author, creator and subject.
-
Social Space and Physical Space: Pierre Bourdieu's Field Theory as a Model for the Social Dynamics of the Built EnvironmentGordon, Lewis R. (Lewis Ricardo), 1962-; Rey, Terry; Margolis, Joseph, 1924-; Gordon, Jane Anna, 1976- (Temple University. Libraries, 2009)The notion of social space or field is a central but under-studied category in the philosopher and sociologist Pierre Bourdieu's theory of practice. The present study of social space is introduced with a contextual account of spatial models in the social sciences prior to Bourdieu that highlights the aptitude for relational spatial models to capture complex social phenomena. It then demonstrates how social space, as an empirically robust and epistemologically intuitive social-scientific model, facilitates the objective representation as well as the subjective understanding of social phenomena. The central thesis is that Bourdieu's reflexive sociology operates in large part by a multiform engagement with the (intuitive or conceptual, but always constructed) apprehension of space, an interpretation that suggests the integration of both physical and social spaces in a unified explanatory framework. A dialectical understanding of the relations between social space and physical space, drawn from the logic of Bourdieu's social theory, is argued for. This philosophical extension of Bourdieu's work is then applied to phenomena in which the reproduction of structures in social space is carried out in and through physical space, and vice versa. Two case studies, the first of office tower districts in contemporary cities and the second of deconstructionist architecture, reveal interactions between social organization and the built environment. The case studies, taken together, also demonstrate the virtue, inherent to a Bourdieuian approach, of explaining both the trends of relative stability and the instances of radical change that are observed in social phenomena.
-
Quantum n-space as a quotient of classical n-spaceGoodearl, KR; Letzter, ES (2000-01-01)The prime and primitive spectra of Oq(fn), the multiparameter quantized coordinate ring of affine n-space over an algebraically closed field k, are shown to be topological quotients of the corresponding classical spectra, specO(fn) and maxo(fn) ≈kn, provided the multiplicative group generated by the entries of q avoids -1. ©2000 American Mathematical Society.
-
Conical Intersections: The Seam Space Between the SciencesMatsika, Spiridoula; Temple University. Honors Program (Temple University. Libraries, 2020)When molecules absorb light and become excited, the energy ultimately has to go somewhere; the energy can be lost by radiation, transferred to another molecule, or lost as heat. To predict how molecules interact with light and other matter, theoretical chemists use calculations based on the Born-Oppenheimer Approximation to numerically estimate energies and other properties of interest. Most processes can be explained within the bounds of the approximation; however, the spontaneous nonadiabatic loss of energy as heat cannot. These non- adiabatic processes are driven by conical intersections and play an important role in many known phenomena. Computationally, conical intersections rise out of the breakdown of the Born- Oppenheimer Approximation and the coupling of electronic and nuclear wavefunctions. Physically, conical intersections represent the seam space of degenerate electronic states on the potential energy surface of a molecule. Metaphorically, conical intersections represent the seam space of the research frontiers in biology, chemistry, physics, mathematics, and computer science. The present work is a review of the work in, and application of, each respective field related to conical intersections and a benchmarking study of the most viable current methods used to calculate conical intersections.